The so-called subband identification method has been introduced recently as an alternative method for identification of finite-impulse response systems with a large tap size. It is known that this method can be more numerically efficent than the classical system identification method, while having a compatible performance. In this paper, we assume a probabilistic framework, and we deal with the following two problems: (1) whether or not the identification result depends on the particular realization of the random process under consideration, and (2) whether or not, the identification algorithm converges to the minimum of the error function. We study these properties by considering both the error functions in individual subbands and a combined error function. We study the critical-sampling and the oversampling cases. We show that optimum convergence is not always guaranteed in the oversampling case. A modification in the identification algorithm will be proposed to fix this problem.